Large-scale computation of elementary flux modes with bit pattern trees

Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays—the ancestors of extreme rays—that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Comparison and improvement of algorithms for computing minimal cut sets

BACKGROUND: Constrained minimal cut sets (cMCSs) have recently been introduced as a framework to enumerate minimal genetic intervention strategies for targeted optimization of metabolic networks. Two different algorithmic schemes (adapted Berge algorithm and binary integer programming) have been proposed to compute cMCSs from elementary modes. However, in their original formulation both algorithms are not fully comparable. RESULTS: Here we show that by a small extension to the integer program both methods become equivalent. Furthermore, based on well-known preprocessing procedures for integer programming we present efficient preprocessing steps which can be used for both algorithms. We then benchmark the numerical performance of the algorithms in several realistic medium-scale metabolic models. The benchmark calculations reveal (i) that these preprocessing steps can lead to an enormous speed-up under both algorithms, and (ii) that the adapted Berge algorithm outperforms the binary integer approach. CONCLUSIONS: Generally, both of our new implementations are by at least one order of magnitude faster than other currently available implementations

Computation of elementary modes: a unifying framework and the new binary approach

BACKGROUND: Metabolic pathway analysis has been recognized as a central approach to the structural analysis of metabolic networks. The concept of elementary (flux) modes provides a rigorous formalism to describe and assess pathways and has proven to be valuable for many applications. However, computing elementary modes is a hard computational task. In recent years we assisted in a multiplication of algorithms dedicated to it. We require a summarizing point of view and a continued improvement of the current methods. RESULTS: We show that computing the set of elementary modes is equivalent to computing the set of extreme rays of a convex cone. This standard mathematical representation provides a unified framework that encompasses the most prominent algorithmic methods that compute elementary modes and allows a clear comparison between them. Taking lessons from this benchmark, we here introduce a new method, the binary approach, which computes the elementary modes as binary patterns of participating reactions from which the respective stoichiometric coefficients can be computed in a post-processing step. We implemented the binary approach in FluxAnalyzer 5.1, a software that is free for academics. The binary approach decreases the memory demand up to 96% without loss of speed giving the most efficient method available for computing elementary modes to date. CONCLUSIONS: The equivalence between elementary modes and extreme ray computations offers opportunities for employing tools from polyhedral computation for metabolic pathway analysis. The new binary approach introduced herein was derived from this general theoretical framework and facilitates the computation of elementary modes in considerably larger networks

The Convex Hull Problem in Practice : Improving the Running Time of the Double Description Method

The double description method is a simple but widely used algorithm for computation of extreme points in polyhedral sets. One key aspect of its implementation is the question of how to efficiently test extreme points for adjacency. In this dissertation, two significant contributions related to adjacency testing are presented. First, the currently used data structures are revisited and various optimizations are proposed. Empirical evidence is provided to demonstrate their competitiveness. Second, a new adjacency test is introduced. It is a refinement of the well known algebraic test featuring a technique for avoiding redundant computations. Its correctness is formally proven. Its superiority in multiple degenerate scenarios is demonstrated through experimental results. Parallel computation is one further aspect of the double description method covered in this work. A recently introduced divide-and-conquer technique is revisited and considerable practical limitations are demonstrated

Elementary approaches to microbial growth rate maximisation

This thesis, called Elementary approaches to microbial growth rate maximisation, reports on a theoretical search for principles underlying single cell growth, in particular for microbial species that are selected for fast growth rates. First, the optimally growing cell is characterised in terms of its elementary modes. We prove an extremum principle: a cell that maximises a metabolic rate uses few Elementary Flux Modes (EFMs, the minimal pathways that support steady-state metabolism). The number of active EFMs is bounded by the number of growth-limiting constraints. Later, this extremum principle is extended in a theory that explicitly accounts for self-fabrication. For this, we had to define the elementary modes that underlie balanced self-fabrication: minimal self-supporting sets of expressed enzymes that we call Elementary Growth Modes (EGMs). It turns out that many of the results for EFMs can be extended to their more general self-fabrication analogue. Where the above extremum principles tell us that few elementary modes are used by a rate-maximising cell, it does not tell us how the cell can find them. Therefore, we also search for an elementary adaptation method. It turns out that stochastic phenotype switching with growth rate dependent switching rates provides an adaptation mechanism that is often competitive with more conventional regulatory-circuitry based mechanisms. The derived theory is applied in two ways. First, the extremum principles are used to review the mathematical fundaments of all optimisation-based explanations of overflow metabolism. Second, a computational tool is presented that enumerates Elementary Conversion Modes. These elementary modes can be computed for larger networks than EFMs and EGMs, and still provide an overview of the metabolic capabilities of an organism

Dynamic Neuromechanical Sets for Locomotion

Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed to find the bounds of possible actuator controls. Previously in the literature, feasible sets analysis has been used in order analyze models assuming static poses. Here, tools that explore the feasible sets of actuator controls over the course of a dynamic task are developed. The cost-function agnostic methods of analysis developed in this work run parallel and in concert with other methods of analysis such as principle components analysis, muscle synergies theory and task prioritization. Researchers and healthcare professionals can gain greater insights into decision making during behavioral tasks by layering these other tools on top of feasible sets analysis

\u3ci\u3eIn silico\u3c/i\u3e Driven Metabolic Engineering Towards Enhancing Biofuel and Biochemical Production

The development of a secure and sustainable energy economy is likely to require the production of fuels and commodity chemicals in a renewable manner. There has been renewed interest in biological commodity chemical production recently, in particular focusing on non-edible feedstocks. The fields of metabolic engineering and synthetic biology have arisen in the past 20 years to address the challenge of chemical production from biological feedstocks. Metabolic modeling is a powerful tool for studying the metabolism of an organism and predicting the effects of metabolic engineering strategies. Various techniques have been developed for modeling cellular metabolism, with the underlying principle of mass balance driving the analysis. In this dissertation, two industrially relevant organisms were examined for their potential to produce biofuels. First, Saccharomyces cerevisiae was used to create biodiesel in the form of fatty acid ethyl esters (FAEEs) through expression of a heterologous acyl-transferase enzyme. Several genetic manipulations of lipid metabolic and / or degradation pathways were rationally chosen to enhance FAEE production, and then culture conditions were modified to enhance FAEE production further. The results were used to identify the rate-limiting step in FAEE production, and provide insight to further optimization of FAEE production. Next, Clostridium thermocellum, a cellulolytic thermophile with great potential for consolidated bioprocessing but a weakly understood metabolism, was investigated for enhanced ethanol production. To accomplish the analysis, two models were created for C. thermocellum metabolism. The core metabolic model was used with extensive fermentation data to elucidate kinetic bottlenecks hindering ethanol production. The genome scale metabolic model was constructed and tuned using extensive fermentation data as well, and the refined model was used to investigate complex cellular phenotypes with Flux Balance Analysis. The work presented within provide a platform for continued study of S. cerevisiae and C. thermocellum for the production of valuable biofuels and biochemicals

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Simulation and database software for computational systems biology : PySCes and JWS Online

Thesis (PhD)--Stellenbosch University, 2005.ENGLISH ABSTRACT: Since their inception, biology and biochemistry have been spectacularly successful in characterising the living cell and its components. As the volume of information about cellular components continues to increase, we need to ask how we should use this information to understand the functioning of the living cell? Computational systems biology uses an integrative approach that combines theoretical exploration, computer modelling and experimental research to answer this question. Central to this approach is the development of computational models, new modelling strategies and computational tools. Against this background, this study aims to: (i) develop a new modelling package: PySCeS, (ii) use PySCeS to study discontinuous behaviour in a metabolic pathway in a way that was very difficult, if not impossible, with existing software, (iii) develop an interactive, web-based repository (JWS Online) of cellular system models. Three principles that, in our opinion, should form the basis of any new modelling software were laid down: accessibility (there should be as few barriers as possible to PySCeS use and distribution), flexibility (pySCeS should be extendable by the user, not only the developers) and usability (PySCeS should provide the tools we needed for our research). After evaluating various alternatives we decided to base PySCeS on the freely available programming language, Python, which, in combination with the large collection of science and engineering algorithms in the SciPy libraries, would give us a powerful modern, interactive development environment.AFRIKAANSE OPSOMMING: Sedert hul totstandkoming was biologie en, meer spesifiek, biochemie uiters suksesvol in die karakterisering van die lewende sel se komponente. Steeds groei die hoeveelheid informasie oor die molekulêre bestanddele van die sel daagliks; ons moet onself dus afvra hoe ons hierdie informasie kan integreer tot 'n verstaanbare beskrywing van die lewende sel se werking. Om dié vraag te beantwoord gebruik rekenaarmatige sisteembiologie 'n geïntegreerde benadering wat teorie, rekenaarmatige modellering en eksperimenteeIe navorsing kombineer. Sentraal tot die benadering is die ontwikkeling van nuwe modelle, strategieë vir modellering, en sagteware. Teen hierdie agtergrond is die hoofdoelstelling van hierdie projek: (i) die ontwikkeling van 'n nuwe modelleringspakket, PySCeS (ii) die benutting van PySCeS om diskontinue gedrag in n metaboliese sisteem te bestudeer (iets wat met die huidiglik beskikbare sagteware redelik moeilik is), (en iii) die ontwikkeling vann interaktiewe, internet-gebaseerde databasis van sellulêre sisteem modelle, JWS Online. Ons is van mening dat nuwe sagteware op drie belangrike beginsels gebaseer behoort te wees: toeganklikheid (die sagteware moet maklik bekombaar en bruikbaar wees), buigsaamheid (die gebruiker moet self PySCeS kan verander en ontwikkel) en bruikbaarheid (al die funksionalitiet wat ons vir ons navorsing nodig moet in PySCeS ingebou wees). Ons het verskeie opsies oorweeg en besluit om die vrylik verkrygbare programmeringstaal, Python, in samehang die groot kolleksie wetenskaplike algoritmes, SciPy, te gebruik. Hierdie kombinasie verskaf n kragtige, interaktiewe ontwikkelings- en gebruikersomgewing. PySCeS is ontwikkel om onder beide die Windows en Linux bedryfstelsels te werk en, meer spesifiek, om gebruik te maak van 'n 'command line interface'. Dit beteken dat PySCeS op enige interaktiewe rekenaar-terminaal Python ondersteun sal werk. Hierdie eienskap maak ook moontlik die gebruik van PySCeS as 'n modelleringskomponent in 'n groter sagteware pakket onder enige bedryfstelsel wat Python ondersteun. PySCeS is op 'n modulere ontwerp gebaseer, wat dit moontlik vir die eindgebruiker maak om die sagteware se bronkode verder te ontwikkel. As 'n toepassing is PySCeS gebruik om die oorsaak van histeretiese gedrag van 'n lineêre, eindproduk-geïnhibeerde metaboliese pad te ondersoek. Ons het hierdie interessante gedrag in 'n vorige studie ontdek, maar kon nie, met die sagteware wat op daardie tydstip tot ons beskikking was, hierdie studie voortsit nie. Met PySCeS se ingeboude vermoë om parameter kontinuering te doen, kon ons die oorsake van hierdie diskontinuë gedrag volledig karakteriseer. Verder het ons 'n nuwe metode ontwikkel om hierdie gedrag te visualiseer as 'n interaksie tussen die volledige sisteem se subkomponente. Tydens PySCeS se ontwikkeling het ons opgemerk dat dit baie moeilik was om metaboliese modelle wat in die literature gepubliseer is te herbou en te bestudeer. Hierdie situasie is grotendeels die gevolg van die feit dat nêrens 'n sentrale databasis vir metaboliese modelle bestaan nie (soos dit wel bestaan vir genomiese data of proteïen strukture). Die JWS Online databasis is spesifiek ontwikkel om hierdie leemte te vul. JWS Online maak dit vir die gebruiker moontlik om, via die internet en sonder die installasie van enige gespesialiseerde modellerings sagteware, gepubliseerde modelle te bestudeer en ook af te laai vir gebruik met ander modelleringspakkette soos bv. PySCeS. JWS Online het alreeds 'n onmisbare hulpbron vir sisteembiologiese navorsing en onderwys geword